Problem: Recently Duff has been a soldier in the army. Malek is her commander.

Their country, Andarz Gu has n cities (numbered from 1 to n) and n - 1 bidirectional roads. Each road connects two different cities. There exist a unique path between any two cities.

There are also m people living in Andarz Gu (numbered from 1 to m). Each person has and ID number. ID number of i - th person is i and he/she lives in city number ci. Note that there may be more than one person in a city, also there may be no people living in the city.

<image>

Malek loves to order. That's why he asks Duff to answer to q queries. In each query, he gives her numbers v, u and a.

To answer a query:

Assume there are x people living in the cities lying on the path from city v to city u. Assume these people's IDs are p1, p2, ..., px in increasing order. 

If k = min(x, a), then Duff should tell Malek numbers k, p1, p2, ..., pk in this order. In the other words, Malek wants to know a minimums on that path (or less, if there are less than a people).

Duff is very busy at the moment, so she asked you to help her and answer the queries.

Input

The first line of input contains three integers, n, m and q (1 ≤ n, m, q ≤ 105).

The next n - 1 lines contain the roads. Each line contains two integers v and u, endpoints of a road (1 ≤ v, u ≤ n, v ≠ u).

Next line contains m integers c1, c2, ..., cm separated by spaces (1 ≤ ci ≤ n for each 1 ≤ i ≤ m).

Next q lines contain the queries. Each of them contains three integers, v, u and a (1 ≤ v, u ≤ n and 1 ≤ a ≤ 10).

Output

For each query, print numbers k, p1, p2, ..., pk separated by spaces in one line.

Examples

Input

5 4 5
1 3
1 2
1 4
4 5
2 1 4 3
4 5 6
1 5 2
5 5 10
2 3 3
5 3 1


Output

1 3
2 2 3
0
3 1 2 4
1 2

Note

Graph of Andarz Gu in the sample case is as follows (ID of people in each city are written next to them):

<image>

Solution (in JAVA):

Solution:
import java.util.*;
import java.math.*;
import java.io.*;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
public class Main {
  static int []head = new int[100001];
  static int []nxt = new int[200001];
  static int []b = new int[200001];
  static int [][]fa = new int[100001][21];
  static int [][][]Fs = new int[100001][21][];
  static ArrayList<Integer> []C = new ArrayList[100001];
  static int k;
  static int []dep = new int[100001];
  static int []cnt = new int[100001];
  static int n;
  static void push(int s, int t) {
    nxt[++k] = head[s];
    head[s] = k;
    b[k] = t;
  }

  static void DEBUG(int n)
  {
    for (int i = 1;i <= n;++i) {
      for (int z = 0;z <= 20;++z) {
        if (fa[i][z] == 0) continue;

        System.out.println("------");
        System.out.println("fa["+i+"]["+z+"]="+fa[i][z]);
        if (Fs[i][z] != null) {
          System.out.println(Arrays.toString(Fs[i][z]));
        }
        System.out.println("------");
      }
    }
    System.out.println("====");
  }


  static void dfs(int x, int f) {
    fa[x][0] = f;
    if (f != 0) {//x root?
      if (C[f].size() > 0) {
        Fs[x][0] = new int[C[f].size()];
        for (int i = 0;i < C[f].size();++i) {
          Fs[x][0][i] = C[f].get(i);
        }
      }
      //Fs[x][0] keeps info (x, fa[x][0]]
    }
    
    for (int i = 1;i <= 20;++i) {
      fa[x][i] = fa[fa[x][i - 1]][i - 1];
      if (Fs[x][i - 1] == null && Fs[fa[x][i - 1]][i - 1] != null) {
        Fs[x][i] = Fs[fa[x][i - 1]][i - 1].clone();
      } else if (Fs[x][i - 1] != null && Fs[fa[x][i - 1]][i - 1] == null) {
        Fs[x][i] = Fs[x][i - 1].clone();
      } else if (Fs[x][i - 1] != null && Fs[fa[x][i - 1]][i - 1] != null) {
        ArrayList<Integer> tmp = new ArrayList<Integer>();
        for (int v:Fs[x][i - 1]) tmp.add(v);
        for (int v:Fs[fa[x][i - 1]][i - 1]) tmp.add(v);
        Collections.sort(tmp);
        while (tmp.size() > 10) tmp.remove(10);
        Fs[x][i] = new int[tmp.size()];
        for (int z = 0;z < tmp.size();++z) {
          Fs[x][i][z] = tmp.get(z);
        }
      }
    }
    dep[x] = dep[f] + 1;
    for (int i = head[x];i > 0;i = nxt[i]) {
      if (b[i] != f) dfs(b[i], x);
    }
  }
  static int LCA(int u,int v, Set<Integer> ans)
  {
    if (dep[u] < dep[v]) {
      int tmp = u;
      u = v;
      v = tmp;
    }
    ans.addAll(C[u]);
    ans.addAll(C[v]);
    int delta = dep[u] - dep[v];
    for(int x = 0;x <= 20;x++) {
      int flag = (1<<x)&delta;
      if(flag > 0) {
        //add info first then u = fa[u][x]
        if (Fs[u][x] != null) for (int it:Fs[u][x]) ans.add(it);
        u = fa[u][x];
      }
    }
    if (u == v) return u;
    for(int x = 20;x >= 0;x--) {
      if(fa[u][x] != fa[v][x]) {
        if (Fs[u][x] != null) for (int it:Fs[u][x]) ans.add(it);
        if (Fs[v][x] != null) for (int it:Fs[v][x]) ans.add(it);
        u=fa[u][x];
        v=fa[v][x];
      }
    }
    ans.addAll(C[fa[u][0]]);
    return fa[u][0];
  }
  static void getans(int x, int f) {
    for (int i = head[x];i > 0;i = nxt[i]) {
      if (b[i] != f) {
        getans(b[i], x); 
        cnt[x] += cnt[b[i]];
      }
    }
  }
  public static void main(String[] args) {
    try {
      MScanner in = new MScanner(System.in);
      BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out, "UTF-8"));
      int n = in.nextInt();
      int m = in.nextInt();
      int q = in.nextInt();
      for (int i = 1;i <= n - 1;++i) {
        int s = in.nextInt();
        int t = in.nextInt();
        push(s, t);
        push(t, s);
      }
      for (int i = 0;i <= n;++i) C[i] = new ArrayList<Integer>();
      for (int i = 1;i <= m;++i) {
        int c = in.nextInt();
        C[c].add(i);
      }
      for (int i = 1;i <= n;++i) {
        if (C[i].size() > 10) {
          Collections.sort(C[i]);
          while (C[i].size() > 10) C[i].remove(10);
        }
      }
      dfs(1, 0);
      //DEBUG(n);
      for (int i = 1;i <= q;++i) {
        int x = in.nextInt();
        int y = in.nextInt();
        int sz = in.nextInt();

        Set<Integer> ans = new TreeSet<>();
        int lca = LCA(x, y, ans);
        int asz = Math.min(ans.size(), sz);
        int cnt = 0;
        out.write(asz + " ");
        for (Integer z:ans) {
          out.write(z + " ");
          if (++cnt >= asz) break;
        }
        out.write("\n");
      }
      out.flush();
      out.close();
    } catch (Exception e) {
      System.out.print(e);
      System.exit(0);
    }
  }
  static class MScanner {
    StringTokenizer st;
    BufferedReader br;
    public MScanner(InputStream system) {
      br = new BufferedReader(new InputStreamReader(system));
    }

    public MScanner(String file) throws Exception {
      br = new BufferedReader(new FileReader(file));
    }

    public String next() throws IOException {
      while (st == null || !st.hasMoreTokens())
	st = new StringTokenizer(br.readLine());
      return st.nextToken();
    }
    public int[] takearr(int n) throws IOException {
      int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
      return in;
    }
    public long[] takearrl(int n) throws IOException {
      long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
      return in;
    }
    public Integer[] takearrobj(int n) throws IOException {
      Integer[]in=new Integer[n];for(int i=0;i<n;i++)in[i]=nextInt();
      return in;
    }
    public Long[] takearrlobj(int n) throws IOException {
      Long[]in=new Long[n];for(int i=0;i<n;i++)in[i]=nextLong();
      return in;
    }
    public String nextLine() throws IOException {
      return br.readLine();
    }

    public int nextInt() throws IOException {
      return Integer.parseInt(next());
    }

    public double nextDouble() throws IOException {
      return Double.parseDouble(next());
    }

    public char nextChar() throws IOException {
      return next().charAt(0);
    }

    public Long nextLong() throws IOException {
      return Long.parseLong(next());
    }

    public boolean ready() throws IOException {
      return br.ready();
    }

    public void waitForInput() throws InterruptedException {
      Thread.sleep(3000);
    }
  }
}